What you will need to listen to a bookmarkable audiobook on your smartphone is a utility that converts the MP3 file into the bookmarkable MP4 format.
If you are an iOS and Mac user, I would recommend using the program Audiobook Binder. It’s a free, open source project that allows you to easily add author/title information, cover artwork and chapter markers while saving it to M4B format so it is identifiable as an audiobook in iTunes and on your iPhone/iPad.
If you’re using Windows, you can convert the MP3 to M4B for listening on your iPhone using the free, open source tool MP3 to iPod/iPhone Audio Book Converter.
For Android users, I would recommend getting the free Android app MortPlayer Audio Books. It let’s you take those pesky one-file MP3 audiobooks and easily bookmark your last place without having to convert them to M4B format.